Linear Algebra Library
Double Precision Real

LINPACK_D, a MATLAB library which solves systems of linear equations for a variety of matrix types and storage modes, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.

MATLAB already provides a wide set of linear equation solvers. This (partial) set of LINPACK routines is provided just for testing and comparison.

LINPACK has officially been superseded by the LAPACK library. The LAPACK library uses more modern algorithms and code structure. However, the LAPACK library can be extraordinarily complex; what is done in a single LINPACK routine may correspond to 10 or 20 utility routines in LAPACK. This is fine if you treat LAPACK as a black box. But if you wish to learn how the algorithm works, or to adapt it, or to convert the code to another language, this is a real drawback. This is one reason I still keep a copy of LINPACK around.

Versions of LINPACK in various arithmetic precisions are available through the NETLIB web site.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


LINPACK_D is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BLAS1_D, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using double precision real arithmetic.

CONDITION, a MATLAB library which implements methods of computing or estimating the condition number of a matrix.

LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.

LINPACK_C, a MATLAB library which solves linear systems using single precision complex arithmetic;


LINPACK_S, a MATLAB library which solves linear systems using single precision real arithmetic;

LINPACK_Z, a MATLAB library which solves linear systems using double precision complex arithmetic;

TEMPLATES, a MATLAB library which carries out simple versions of various iterative solvers.

TEST_MAT, a MATLAB library which defines test matrices.

TEST_MATRIX, a MATLAB library which contains a collection of test matrices by Nick Higham.

TOEPLITZ_CHOLESKY, a MATLAB library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.

WATHEN, a MATLAB library which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, Linpack, conjugate gradient) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).


Original FORTRAN77 version by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. MATLAB version by John Burkardt.


  1. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
    LINPACK User's Guide,
    SIAM, 1979,
    ISBN13: 978-0-898711-72-1,
    LC: QA214.L56.
  2. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
    Algorithm 539, Basic Linear Algebra Subprograms for Fortran Usage,
    ACM Transactions on Mathematical Software,
    Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

Utilities and BLAS1 routines:

Last revised on 16 February 2019.